Kolmogorov Arnold Networks (KANs) are an emerging architecture for building machine learning models. KANs are based on the theoretical foundation of the Kolmogorov-Arnold Theorem and its expansions, which provide an exact representation of a multi-variate continuous bounded function as the composition of a limited number of univariate continuous functions. While such theoretical results are powerful, their use as a representation learning alternative to a multi-layer perceptron (MLP) hinges on the ad-hoc choice of the number of bases modeling each of the univariate functions. In this work, we show how to address this problem by adaptively learning a potentially infinite number of bases for each univariate function during training. We therefore model the problem as a variational inference optimization problem. Our proposal, called InfinityKAN, which uses backpropagation, extends the potential applicability of KANs by treating an important hyperparameter as part of the learning process.

We consider the following classification problem: Given a population of individuals characterized by a set of attributes represented as a vector in ${\mathbb R}^N$, the goal is to find a hyperplane in ${\mathbb R}^N$ that separates two sets of points corresponding to two distinct classes. This problem, with a history dating back to the perceptron model, remains central to machine learning. In this paper we propose a novel approach by searching for a vector of parameters in a bounded $N$-dimensional hypercube centered at the origin and a positive vector in ${\mathbb R}^M$, obtained through the minimization of an entropy-based function defined over the space of unknown variables. The method extends to polynomial surfaces, allowing the separation of data points by more complex decision boundaries. This provides a robust alternative to traditional linear or quadratic optimization techniques, such as support vector machines and gradient descent. Numerical experiments demonstrate the efficiency and versatility of the method in handling diverse classification tasks, including linear and non-linear separability.

Ordinal classification problems, where labels exhibit a natural order, are prevalent in high-stakes fields such as medicine and finance. Accurate uncertainty quantification, including the decomposition into aleatoric (inherent variability) and epistemic (lack of knowledge) components, is crucial for reliable decision-making. However, existing research has primarily focused on nominal classification and regression. In this paper, we introduce a novel class of measures of aleatoric and epistemic uncertainty in ordinal classification, which is based on a suitable reduction to (entropy- and variance-based) measures for the binary case. These measures effectively capture the trade-off in ordinal classification between exact hit-rate and minimial error distances. We demonstrate the effectiveness of our approach on various tabular ordinal benchmark datasets using ensembles of gradient-boosted trees and multi-layer perceptrons for approximate Bayesian inference. Our method significantly outperforms standard and label-wise entropy and variance-based measures in error detection, as indicated by misclassification rates and mean absolute error. Additionally, the ordinal measures show competitive performance in out-of-distribution (OOD) detection. Our findings highlight the importance of considering the ordinal nature of classification problems when assessing uncertainty.

Social media popularity prediction plays a crucial role in content optimization, marketing strategies, and user engagement enhancement across digital platforms. However, predicting post popularity remains challenging due to the complex interplay between visual, textual, temporal, and user behavioral factors. This paper presents HyperFusion, a hierarchical multimodal ensemble learning framework for social media popularity prediction. Our approach employs a three-tier fusion architecture that progressively integrates features across abstraction levels: visual representations from CLIP encoders, textual embeddings from transformer models, and temporal-spatial metadata with user characteristics. The framework implements a hierarchical ensemble strategy combining CatBoost, TabNet, and custom multi-layer perceptrons. To address limited labeled data, we propose a two-stage training methodology with pseudo-labeling and iterative refinement. We introduce novel cross-modal similarity measures and hierarchical clustering features that capture inter-modal dependencies. Experimental results demonstrate that HyperFusion achieves competitive performance on the SMP challenge dataset. Our team achieved third place in the SMP Challenge 2025 (Image Track). The source code is available at https://anonymous.4open.science/r/SMPDImage.

Explicit structural information has been proven to be encoded by Graph Neural Networks (GNNs), serving as auxiliary knowledge to enhance model capabilities and improve performance in downstream NLP tasks. However, recent studies indicate that GNNs fail to fully utilize structural information, whereas Multi-Layer Perceptrons (MLPs), despite lacking the message-passing mechanisms inherent to GNNs, exhibit a surprising ability in structure-aware tasks. Motivated by these findings, this paper introduces a comprehensive probing framework from an information-theoretic perspective. The framework is designed to systematically assess the role of explicit structural modeling in enhancing language model (LM) representations and to investigate the potential of MLPs as efficient and scalable alternatives to GNNs. We extend traditional probing classifiers by incorporating a control module that allows for selective use of either the full GNN model or its decoupled components, specifically, the message-passing and feature-transformation operations.This modular approach isolates and assesses the individual contributions of these operations, avoiding confounding effects from the complete GNN architecture. Using the Edge Probing Suite, a diagnostic tool for evaluating the linguistic knowledge encoded in LMs, we find that MLPs, when used as feature-transformation modules, consistently improve the linguistic knowledge captured in LM representations across different architectures. They effectively encode both syntactic and semantic patterns. Similarly, GNNs that incorporate feature-transformation operations show beneficial effects. In contrast, models that rely solely on message-passing operations tend to underperform, often leading to negative impacts on probing task performance.

The Lipschitz constant of a neural network is connected to several important properties of the network such as its robustness and generalization. It is thus useful in many settings to estimate the Lipschitz constant of a model. Prior work has focused mainly on estimating the Lipschitz constant of multi-layer perceptrons and convolutional neural networks. Here we focus on data modeled as sets or multisets of vectors and on neural networks that can handle such data. These models typically apply some permutation invariant aggregation function, such as the sum, mean or max operator, to the input multisets to produce a single vector for each input sample. In this paper, we investigate whether these aggregation functions are Lipschitz continuous with respect to three distance functions for unordered multisets, and we compute their Lipschitz constants. In the general case, we find that each aggregation function is Lipschitz continuous with respect to only one of the three distance functions. Then, we build on these results to derive upper bounds on the Lipschitz constant of neural networks that can process multisets of vectors, while we also study their stability to perturbations and generalization under distribution shifts. To empirically verify our theoretical analysis, we conduct a series of experiments on datasets from different domains.

Kolmogorov Arnold Networks (KANs), built upon the Kolmogorov Arnold representation theorem (KAR), have demonstrated promising capabilities in expressing complex functions with fewer neurons. This is achieved by implementing learnable parameters on the edges instead of on the nodes, unlike traditional networks such as Multi-Layer Perceptrons (MLPs). However, KANs potential in quantum machine learning has not yet been well explored. In this work, we present an implementation of these KAN architectures in both hybrid and fully quantum forms using a Quantum Circuit Born Machine (QCBM). We adapt the KAN transfer using pre-trained residual functions, thereby exploiting the representational power of parametrized quantum circuits. In the hybrid model we combine classical KAN components with quantum subroutines, while the fully quantum version the entire architecture of the residual function is translated to a quantum model. We demonstrate the feasibility, interpretability and performance of the proposed Quantum KAN (QuKAN) architecture.

We study classical asymmetric binary perceptron (ABP) and associated \emph{local entropy} (LE) as potential source of its algorithmic hardness. Isolation of \emph{typical} ABP solutions in SAT phase seemingly suggests a universal algorithmic hardness. Paradoxically, efficient algorithms do exist even for constraint densities $α$ fairly close but at a finite distance (\emph{computational gap}) from the capacity. In recent years, existence of rare large dense clusters and magical ability of fast algorithms to find them have been posited as the conceptual resolution of this paradox. Monotonicity or breakdown of the LEs associated with such \emph{atypical} clusters are predicated to play a key role in their thinning-out or even complete defragmentation. Invention of fully lifted random duality theory (fl RDT) [90,93,94] allows studying random structures \emph{typical} features. A large deviation upgrade, sfl LD RDT [96,97], moves things further and enables \emph{atypical} features characterizations as well. Utilizing the machinery of [96,97] we here develop a generic framework to study LE as an ABP's atypical feature. Already on the second level of lifting we discover that the LE results are closely matching those obtained through replica methods. For classical zero threshold ABP, we obtain that LE breaks down for $α$ in $(0.77,0.78)$ interval which basically matches $α\sim 0.75-0.77$ range that currently best ABP solvers can handle and effectively indicates that LE's behavior might indeed be among key reflections of the ABP's computational gaps presumable existence.

Mixture of Experts (MoE) architectures increase large language model scalability, yet their performance depends on the router module that moves tokens to specialized experts. Bad routing can load imbalance and reduced accuracy. This project designed and implemented different router architectures within Transformer models to fix these limitations. We experimented with six distinct router variants Linear, Attention, Multi-Layer Perceptron (MLP), Hybrid, Hash, and our new MLP-Hadamard. We characterized these routers using BERT and the Qwen1.5-MoE model, looking at parameter efficiency, inference latency, routing entropy, and expert utilization patterns. Our evaluations showed distinct trade-offs: Linear routers offer speed, while MLP and Attention routers provide greater expressiveness. The MLP-Hadamard router shows a unique capability for structured, sparse routing. We successfully replaced and fine-tuned custom routers within the complex, quantized Qwen1.5-MoE model. This work provides a comparative analysis of MoE router designs and offers insights into optimizing their performance for efficient and effective large-scale model deployment.

This study introduces a framework that integrates nonlinear feature extraction, classification, and efficient optimization. First, kernel principal component analysis with a radial basis function kernel reduces dimensionality while preserving 95% of the variance. Second, a multilayer perceptron (MLP) learns to predict disease status. Finally, a modified multiprocessing genetic algorithm (MIGA) optimizes MLP hyperparameters in parallel over ten generations. We evaluated this approach on three datasets: the Wisconsin Diagnostic Breast Cancer dataset, the Parkinson's Telemonitoring dataset, and the chronic kidney disease dataset. The MLP tuned by the MIGA achieved the best accuracy of 99.12% for breast cancer, 94.87% for Parkinson's disease, and 100% for chronic kidney disease. These results outperform those of other methods, such as grid search, random search, and Bayesian optimization. Compared with a standard genetic algorithm, kernel PCA revealed nonlinear relationships that improved classification, and the MIGA's parallel fitness evaluations reduced the tuning time by approximately 60%. The genetic algorithm incurs high computational cost from sequential fitness evaluations, but our multiprocessing interface GA (MIGA) parallelizes this step, slashing the tuning time and steering the MLP toward the best accuracy score of 99.12%, 94.87%, and 100% for breast cancer, Parkinson's disease, and CKD, respectively.